New Republican National Committee Chairman Reince Priebus said Tuesday that the GOP’s potential presidential candidates such as Donald Trump have a right to make claims about President Obama’s birth certificate, and he is not going to play referee as the party struggles to settle on a 2012 nominee.

Mr. Priebus said he thinks the field of candidates will be defined by the end of the summer, and there could come a time when he has to reel someone in; but for now, he believes the hopefuls should be allowed to make their own cases - and that includes Mr. Trump’s attacks on the president.

“Of course you want your candidates to play nice in the sandbox, but the reality is you have to allow everybody the opportunity to be who they are. You have to allow your candidates to make the case that they want to make to the primary voters, and then you allow the primary voters to choose a candidate,” the RNC chief told reporters at a breakfast sponsored by the Christian Science Monitor.

Elected party chairman earlier this year, Mr. Priebus is the unofficial ringmaster of the 2012 Republican campaign and primary season circus, complete with fights among states over the timing of primaries, and battles among news outlets, state parties and presidential campaigns over who will host candidate debates.

The field is slowly taking shape, with Texas Rep. Ron Paul, a two-time presidential candidate, announcing in Iowa on Tuesday that he will form an exploratory committee to test another run. On Monday, meanwhile, Mississippi Gov. Haley Barbour said he will not seek the GOP’s nomination.

Former New York Mayor Rudolph W. Giuliani, whose 2008 bid flamed out, told The Washington Times he is leaving open the chance to run again if he decides the field isn’t strong enough.

“I keep in contact with people in New Hampshire and try to figure out what kind of a chance I have,” Mr. Giuliani said in an interview. “At this point, I’m not actively considering it, but I have the door open.”

Mr. Giuliani had praise for fellow his New Yorker Mr. Trump, calling him “the most exciting candidate in the race,” adding that he is “saying things the American people need to hear.” But Mr. Giuliani distanced himself from Mr. Trump’s focus on Mr. Obama’s birth.

“I’m not one who wants to raise that question,” he said. “It’s been proven to my satisfaction that the president was born in the United States.”

The focus on Mr. Obama’s birth raises a tough question for Republican officials struggling to balance their party’s right wing, which is energized after the 2010 elections, and the swing voters who will likely decide the presidential contest next year.

Media organizations have investigated charges Mr. Obama was not born in Hawaii and concluded they are unfounded. And Mr. Obama has released a copy of a certificate of live birth from Hawaii, which is considered legal proof of the president’s birthplace.

Despite that evidence, many Republican voters still question his birth, and Mr. Trump in particular has ridden the issue to prominence in the nascent GOP presidential field.

On Tuesday, White House press secretary Jay Carney dismissed the charges as “an unfortunate distraction from the issues that I think most Americans care about.”

Mr. Priebus, a former chairman of Wisconsin’s GOP, said he has seen rough-and-tumble primaries in that state before and hopes to set an orderly nominating process for 2012.

He said one priority is to establish a limited number of officially sanctioned candidate debates, starting this summer, much as the Democratic Party did in 2007 and 2008.